Low-dimensional models of turbulence or, the dynamics of coherent structures (Q2776596)

The authors present an approach to the construction of models of turbulent energy production, focussing on flows energetically dominated by coherent structures. The low-dimensional dynamical systems describing the interactions among small sets of such structures are studied via techniques of dynamical systems theory, where the main tool is the Karhunen-Loeve or proper orthogonal decomposition, which provides a basis for convergence-optimal representations of complex spatio-temporal fields. The analysis of bifurcations, invariant structures and attractors in the phase spaces of these (relatively) tractable systems allows to gain insight into physical mechanisms of turbulence production. Special attention is paid to heteroclinic cycles and symmetries inherited from the original physical system and governing evolution (e.g. Kuramoto-Sivashinsky) equations. In particular, the authors examine random perturbations of heteroclinic cycles, and show that the effect of outher boundary layer on the near-wall region can be described by a quasi-random pressure field at the outer edge of that region.NEWLINENEWLINEFor the entire collection see [Zbl 0977.00028].